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arXiv:2111.12219 · Quantum Information Processing

Performance of Grover’s search algorithm with diagonalizable collective noises

Minghua Pan, Tian‐Jian Xiong, Shenggen Zheng

Published Jun 7, 2023• 8 citations
arXivHTMLPDF
DOI
10.1007/s11128-023-03994-3

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Abstract The article proposes a modification of Grover’s quantum oracle quantum search algorithm, which makes it easier to search the database. The algorithm is implemented in the Python programming language using the Reggeti Forest cloud quantum service. The authors of the article use the mean flipping method, which solves the search problem during the iterative order √ (2 ^ n). Development offers great potential for the practical application of the Grover quantum algorithm, as it is characterized by higher performance and speed when performing research. Theoretically, the algorithm provides quadratic acceleration compared to conventional computers. It is not an exponential acceleration, but it remains important for large data carriers. The quantum parallelism of the Grover search algorithm is based on a simultaneous change in the amplitudes of all the inputs. This is done through a superposition of states, which is a purely quantum concept. In addition, the research is carried out globally, which indicates a significant improvement in optimization procedures. Grover’s algorithm, on the other hand, is sensitive to the number of iterations. The more iterations, the smaller the amplitude of the correct answer, so the wrong choice of this parameter can digest the solution. In addition, the operation of the algorithm is limited in the case of the introduction of noise into a quantum system, which is real in modern quantum computers.

IOP Conference Series Materials Science and Engineering•Dec 1, 2020•1 citation
Quantum computing holds the potential to provide speedups in solving complex problems that are currently difficult for classical computers. However, the realization of this potential is hindered by the issue of current hardware reliability, primarily due to noise and architectural imperfections. As quantum computing systems rapidly advance, there exists a need to create a generalizable benchmarking tool that can assess reliability across different hardware platforms. In this paper, we introduce GRADE (Grover-based Reliability Assessment for Device Evaluation), an open-source benchmarking toolkit to evaluate the reliability of quantum hardware using a generalized form of Grover's algorithm. GRADE operates by implementing Grover's algorithm to search through a variety of primitive collections that are customizable by the user, analyzing the probability distribution of the results to assess accuracy and stability. This approach aims to evaluate the hardware performance of Grover's algorithm, which is fundamental in unordered search problems, making it an ideal candidate for benchmarking purposes, as it is one of the few generalizable quantum algorithms that provide a direct speedup. Importantly, GRADE can adapt to a wide range of quantum computing platforms, ensuring it can be applied across different hardware architectures. Additionally, our work provides a scoring function for evaluating the hardware performance for multi-target Grover's implementation. Our work validates this approach across a multitude of simulators and hardware platforms from varying providers, demonstrating its adaptability to differing backend providers.
This work tests the performance of Grover’s search circuits on some IBM superconducting quantum devices in case of the size of search space N = 16 and N = 32. Ideally, we expect to get an outcome probability distribution that is clearly peaked at the goal (marked) state. However, the quantum circuit executed on real devices is vulnerable to noise which leads to fluctuations in the results. The contributions of this paper are therefore the following: a) it presents two new Grover’s search circuits for N = 16 which were not yet reported in the state of the art; b) it shows performance difference between simulation results and results obtained on real devices; c) it shows the need of adding error correction on the circuit for N ≥ 32.
Abstract The article proposes a modification of Grover’s quantum oracle quantum search algorithm, which makes it easier to search the database. The algorithm is implemented in the Python programming language using the Reggeti Forest cloud quantum service. The authors of the article use the mean flipping method, which solves the search problem during the iterative order √ (2 ^ n). Development offers great potential for the practical application of the Grover quantum algorithm, as it is characterized by higher performance and speed when performing research. Theoretically, the algorithm provides quadratic acceleration compared to conventional computers. It is not an exponential acceleration, but it remains important for large data carriers. The quantum parallelism of the Grover search algorithm is based on a simultaneous change in the amplitudes of all the inputs. This is done through a superposition of states, which is a purely quantum concept. In addition, the research is carried out globally, which indicates a significant improvement in optimization procedures. Grover’s algorithm, on the other hand, is sensitive to the number of iterations. The more iterations, the smaller the amplitude of the correct answer, so the wrong choice of this parameter can digest the solution. In addition, the operation of the algorithm is limited in the case of the introduction of noise into a quantum system, which is real in modern quantum computers.